1. Field of the Disclosure
The disclosure relates generally to micromechanical devices or micro-electromechanical systems (MEMS) and, more particularly, to micromechanical or MEMS resonators.
2. Brief Description of Related Technology
MEMS resonators are attractive for use in many applications as a cost-effective replacement for discrete devices such as quartz crystal oscillators or surface-acoustic wave (SAW) resonators. MEMS resonators are particularly promising for use in integrated frequency reference and timing devices, as MEMS resonators can be fabricated alone or on substrates with other circuitry, such as MOS or bipolar circuits. MEMS resonators can also have very high mechanical quality factors (Q), which lead to good frequency selectivity.
MEMS resonators have also been used to replace quartz crystal oscillators in several clock and timing applications. Some of these applications demand excellent frequency stability across a wide range of environmental conditions. For example, certain clock and timing applications call for oscillators stable to a few to tens of parts per million (ppm) over a temperature range from about −40° C. to about 85° C. or even about −55° C. to about 125° C.
The high-Q nature of MEMS resonators and normal fabrication process variations lead to challenges in fabricating MEMS resonators with frequency accuracy better than a few percent. The resonant frequency of a MEMS resonator is determined by its physical characteristics, which are, in turn, functions of design, materials, and the processing methods used to fabricate the resonator. Due to the small size of MEMS resonators and the material properties of silicon, the frequency of a MEMS resonator is sensitive to temperature variations.
Electrostatic MEMS resonators are also sensitive to variations resulting from the manufacturing process. In electrostatically driven MEMS resonators, a bias voltage is applied to the resonator between a resonator body and a driving electrode, and an AC signal is applied to the driving electrode. Once the frequency of the AC signal equals the natural resonant frequency of the resonator, the resonator starts to vibrate at the resonant frequency. The gap between the driving electrode and the resonator body and the spring constant of the resonator body are two parameters that affect resonator operation. Each parameter is subject to manufacturing process variation.